This weekend they face a Samoa side who, like Italy, are a rugby nation on the way up and who will be boosted by victory over Scotland last Saturday.
And Zanni is only too aware of the danger posed to his side.
"We allowed South Africa to dictate the game in the first half," said Zanni. "That was a mistake you can't afford to do that, especially against a team like them.
"After the break we reorganised but we still made some mistakes with the ball and in our tactical game.
"There are more negatives than positives from Saturday but it's a good stimulus to prepare in the best possible way for the game against Samoa.
"You can forget about the big, quick, disorganised Samoan sides of the past. This team that beat Scotland, it big and quick but they know exactly what to do on the pitch. They have improved every part of their game and we saw against Scotland that they are in great form."
Zanni is joined in the Italy starting XV by Treviso teammates Edoardo Gori, Tommaso Iannone, Valerio Bernabo as well as front rows Leonardo Ghiraldini and Alberto de Marchi.
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